La correspondance de McKay

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1. [Ba1] V. Batyrev, Birational Calabi-Yau n-folds have equal Betti numbers, in New trends in algebraic geometry, Klaus Hulek and others (eds.), CUP, 1999, pp. 1-11. Zbl0955.14028MR1714818
2. [Ba2] V. Batyrev, Stringy Hodge numbers of varieties with Gorenstein canonical singularities, in Integrable systems and algebraic geometry (Kobe/Kyoto, 1997), 1-32, World Sci. Publishing, River Edge, NJ, 1998. Zbl0963.14015MR1672108
3. [Ba3] V. Batyrev, Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs, J. Eur. Math. Soc.1 (1999), 5-33. Zbl0943.14004MR1677693
4. [BD] V. Batyrev and D. Dais, Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry, Topology35 (1996), 901-929. Zbl0864.14022MR1404917
5. [BO1] A. Bondal and D. Orlov, Reconstruction of a variety from the derived category and groups of autoequivalences, Max Planck Inst. Bonn preprint MPI-97-36, math.AG/9712029, 20 pp. MR1818984
6. [BO2] A. Bondal and D. Orlov, Semi-orthogonal decomposition for algebraic varieties, preprint alg-geom/9506012. 
7. [Br] T. Bridgeland, Equivalences of triangulated categories and Fourier-Mukai transforms, Bull. London Math. Soc.31 (1999), 25-34. Zbl0937.18012MR1651025
8. [BrM] T. Bridgeland and A. Maciocia, Fourier-Mukai transforms for K3 fibrations, preprint math/9908022, 18 pp. Zbl1066.14047
9. [B] J.-L. Brylinski, A correspondence dual to McKay's, preprint alg-geom/9612003. 
10. [BKR] T. Bridgeland, A. King and M. Reid, Mukai implies McKay, preprint math/9908027, 17 pp. 
11. [C1] A. Craw, An introduction to motivic integration, preliminary draft available from www.maths.warwick.ac.uk/~craw, 23 pp. MR2103724
12. [C2] A. Craw, A-Hilb C3 and McKay correspondence, work in progress. 
13. [CR] A. Craw and M. Reid, How to calculate A-Hilb C3, preprint math/ 9909085, 29 pp. MR2075608
14. [DHVW] L. Dixon, J. Harvey, C. Vafa and E. Witten, Strings on orbifolds. I, Nuclear Phys.B261 (1985), 678-686. II, same J.274 (1986), 285-314. MR818423
15. [DHZ] D.I. Dais, M. Henk and G.M. Ziegler, All Abelian quotient c.i. singularities admit crepant resolutions, preprint alg-geom/9704007, 35 pp. 
16. [DL1] J. Denef and F. Loeser, Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math.135 (1999), 201-232. Zbl0928.14004MR1664700
17. [DL2] J. Denef and F. Loeser, Motivic integration, quotient singularities and the McKay correspondence, preprint math/9903187, 20 pp., to appear in Compositio Math. Zbl1080.14001MR1905024
18. [GSpV] G. Gonzalez-Sprinberg and J.-L. Verdier, Construction géométrique de la correspondance de McKay, Ann. Sci. École Norm. Sup. (4) 16 (1983), 409-449. Zbl0538.14033MR740077
19. [H] R. Hartshorne, Residues and duality, L.N.M.20Springer, 1966. Zbl0212.26101MR222093
20. [HH] F. Hirzebruch and T. Höfer, On the Euler number of an orbifold, Math. Ann.286 (1990), 255-260. Zbl0679.14006MR1032933
21. [IN] Y. Ito and H. Nakajima, McKay correspondence and Hilbert schemes in dimension three, preprint math.AG/9803120, 35 pp., to appear in Topology. Zbl0995.14001MR1783852
22. [IN1] Y. Ito and I. Nakamura, McKay correspondence and Hilbert schemes, Proc. Japan Acad. Ser. A Math. Sci.72 (1996), 135-138. Zbl0881.14002MR1420598
23. [IN2] Y. Ito and I. Nakamura, Hilbert schemes and simple singularities, in New trends in algebraic geometry, Hulek and others (eds.), CUP1999, pp. 155-233. Zbl0954.14001MR1714824
24. [IR] Y. Ito and M. Reid, The McKay correspondence for finite subgroups of SL(3,C), in Higher-dimensional complex varieties (Trento, 1994), 221- 240, de Gruyter, Berlin, 1996. Zbl0894.14024MR1463181
25. [K] M. Kontsevich, Motivic integration, Legendary lecture at Orsay, Thu 7th Dec 1995. 
26. [Ka1] D. Kaledin, McKay correspondence for symplectic quotient singularities, preprint math/9907087, 28 pp. MR1892847
27. [Ka2] D. Kaledin, Dynkin diagrams and crepant resolutions of quotient singularities, preprint math/9903157, 30 pp. 
28. [Kr] P.B. Kronheimer, The construction of ALE spaces as hyper-Kähler quotients, J. Diff. Geom.29 (1989), 665-683. Zbl0671.53045MR992334
29. [GIT] D. Mumford, J. Fogarty and F. Kirwan, Geometric invariant theory (3rd edn.), Springer, 1994. ' Zbl0797.14004MR1304906
30. [Mu] S. Mukai, Duality between D(X) and D(X) with its application to Picard sheaves, Nagoya Math. J.81 (1981), 153-175. Zbl0417.14036MR607081
31. [N] I. Nakamura, Hilbert schemes of Abelian group orbits, to appear in J. Alg. Geom. Zbl1104.14003MR1838978
32. [O] D.O. Orlov, Equivalences of derived categories and K3 surfaces, Algebraic geometry, 7J. Math. Sci. (New York) 84 (1997), 1361-1381, preprint alg-geom/9606006, 28 pp. Zbl0938.14019MR1465519
33. [YPG] M. Reid, Young person's guide to canonical singularities, in Algebraic Geometry, Bowdoin 1985, ed. S. Bloch, Proc. of Symposia in Pure Math.46, A.M.S. (1987), vol. 1, 345-414. Zbl0634.14003MR927963
34. [R] M. Reid, McKay correspondence, in Proc. of algebraic geometry symposium (Kinosaki, Nov 1996), T. Katsura (ed.), 14-41, preprint alggeom/9702016, 30 pp. 
35. [Homework] Homework sheets will be on my website www.maths.warwick.ac.uk/~miles, including examples, exercises, more hints, and errata to this lecture. 
36. [Roan] S.-S. Roan, Orbifold Euler characteristic, in Mirror symmetry, II, AMS1997, pp. 129-140. Zbl0939.14020MR1416337
37. [T] B. Totaro, Chern numbers for singular varieties and elliptic homology. Ann. of Math.151 (2000), no. 2, 757-791. Preprint available from www.dpmms.cam.ac.uk/~bt219. Zbl1050.14500MR1765709
38. [V] C. Vafa, String vacua and orbifoldized LG models, Modern Phys. Lett.A4 (1989), 1169-1185. MR1016963
39. [Vb] M. Verbitsky, Holomorphic symplectic geometry and orbifold singularities, preprint math. AG/9903175, 17 pp. MR1796694
40. [Z] E. Zaslow, Topological orbifold models and quantum cohomology rings, Comm. Math. Phys.156 (1993), 301-331. Zbl0795.53074MR1233848

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